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Questions in mathematics

[Answered] Approximate the integral with your calculator. Round the answer to the nearest thousandth. $\int_1^4(\ln x)^3 d x \approx[?]$

[Answered] Answer the following questions for the function [tex]f(x)=x \sqrt{x^2+25}[/tex] defined on the interval [tex]-5 \leq x \leq 5[/tex]. [tex]f(x)[/tex] is concave down on the interval [tex]x=[/tex] $\square$ to [tex]x=[/tex] $\square$ [tex]f(x)[/tex] is concave up on the interval [tex]x=[/tex] $\square$ to [tex]x=[/tex] $\square$ The inflection point for this function is at [tex]x=[/tex] $\square$ The minimum for this function occurs at [tex]x=[/tex] $\square$ The maximum for this function occurs at [tex]x=[/tex] $\square$

[Answered] Given that $u=x+1$, which integral is equivalent to $\int \frac{x^2}{\sqrt{x+1}} d x$ ? a $\int(\sqrt{u^3}+\frac{1}{\sqrt{u}}) d u$ b $\int(\sqrt{u^3}-2 \sqrt{u}+\frac{1}{\sqrt{u}}) d u$ c $\int(\sqrt{u^3}-2 \sqrt{u}) d u$ d $\int(\sqrt{u^3}-2 \sqrt{u^2}+\frac{1}{u}) d u$ e $\int(\frac{1}{\sqrt{u}}-2 \sqrt{u}) d u$

[Answered] A learn-to-type software program claims that it can improve your typing skills. To test the claim and possibly help yourself out, you and eight of your friends decide to try the program and see what happens. Use the table below to construct a $95 \%$ confidence interval for the true mean change in the typing speeds for people who have completed the typing program. Let Population 1 be the typing speed before taking the program and Population 2 be the typing speed after taking the program. Round the endpoints of the interval to one decimal place, if necessary. | | | | :----- | :----- | | Typing Speeds (in Words per Minute) | | | Before | After | | 30 | 39 | | 35 | 53 | | 33 | 32 | | 45 | 54 | | 40 | 35 | | 31 | 30 | | 40 | 44 | | 39 | 50 | | 55 | 55 |

[Answered] Which equation represents a line that passes through $(-9,-3)$ and has a slope of $-6$? A. $y-9=-6(x-3)$ B. $y+9=-6(x+3)$ C. $y-3=-6(x-9)$ D. $y+3=-6(x+9)$

[Answered] Which is equivalent to $\sqrt[4]{9}^{\frac{1}{2} x}$ ? A. $9^{2 x}$ B. $9^{\frac{1}{8} x}$ C. $\sqrt{9}^x$ D. $\sqrt[6]{9}^x$

[Answered] X(x-2)^2(x*4) When expanded what is final product? I need step by step on how to do this please

[Answered] Find the L.C.M and G.C.D of [tex]$2^3 \times 3^2 \times 5 \times 7$[/tex] and [tex]$2^2 \times 3^2 \times 5^2 \times 7$[/tex] and leave your answer in power form

[Answered] The area of a square game board is 144 sq. in. What's the length of the sides of the board? A. 8 in. B. 72 in. C. 36 in. D. 12 in.

[Answered] Given two dependent random samples with the following results: | Population 1 | 30 | 47 | 19 | 49 | 42 | 31 | 24 | |---|---|---|---|---|---|---|---| | Population 2 | 45 | 37 | 29 | 44 | 46 | 46 | 34 | Use this data to find the $90 \%$ confidence interval for the true difference between the population means. Assume that both populations are normally distributed. Step 1 of 4: Find the point estimate for the population mean of the paired differences. Let $x_1$ be the value from Population 1 and $x_2$ be the value from Population 2 and use the formula $d=x_2-x_1$ to calculate the paired differences. Round your answer to one decimal place.